Universality for a class of random band matrices

Paul Bourgade; Laszlo Erdoos; Horng Tzer Yau; Jun Yin

doi:10.4310/ATMP.2017.v21.n3.a5

Universality for a class of random band matrices

Paul Bourgade, Laszlo Erdoos, Horng Tzer Yau, Jun Yin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.

Original language	English (US)
Pages (from-to)	739-800
Number of pages	62
Journal	Advances in Theoretical and Mathematical Physics
Volume	21
Issue number	3
DOIs	https://doi.org/10.4310/ATMP.2017.v21.n3.a5
State	Published - 2017

Keywords

Band matrices
Dyson Brownian motion
Quantum unique ergodicity
Universality

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

Access to Document

10.4310/ATMP.2017.v21.n3.a5

Cite this

@article{06971c770e304260b2a7790853520ca0,

title = "Universality for a class of random band matrices",

abstract = "We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.",

keywords = "Band matrices, Dyson Brownian motion, Quantum unique ergodicity, Universality",

author = "Paul Bourgade and Laszlo Erdoos and Yau, {Horng Tzer} and Jun Yin",

year = "2017",

doi = "10.4310/ATMP.2017.v21.n3.a5",

language = "English (US)",

volume = "21",

pages = "739--800",

journal = "Advances in Theoretical and Mathematical Physics",

issn = "1095-0761",

publisher = "International Press, Inc.",

number = "3",

}

TY - JOUR

T1 - Universality for a class of random band matrices

AU - Bourgade, Paul

AU - Erdoos, Laszlo

AU - Yau, Horng Tzer

AU - Yin, Jun

PY - 2017

Y1 - 2017

N2 - We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.

AB - We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.

KW - Band matrices

KW - Dyson Brownian motion

KW - Quantum unique ergodicity

KW - Universality

UR - http://www.scopus.com/inward/record.url?scp=85028353753&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028353753&partnerID=8YFLogxK

U2 - 10.4310/ATMP.2017.v21.n3.a5

DO - 10.4310/ATMP.2017.v21.n3.a5

M3 - Article

AN - SCOPUS:85028353753

SN - 1095-0761

VL - 21

SP - 739

EP - 800

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

IS - 3

ER -

Universality for a class of random band matrices

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this